1. Field of the Invention
The present invention relates to an optical coupling apparatus for introducing and coupling incident light to a wave guide.
2. Description of the Prior Art
A prior art optical coupling apparatus will be explained at first referring to, for instance, that disclosed in PCT laid-open publication No. WO 89/06424 which employs a so-called grating coupling method.
FIG. 4 is a schematical cross-sectional view of the conventional optical coupling apparatus. Light of a wavelength .lambda. emitted from a laser diode 1 is converted into a parallel beam 6A by a condenser lens 2 and is then converted, via a polarizer device 3, into a circumferentially polarized beam 6C in which the electric field vectors are oriented in tangential directions of concentric circles. The polarized beam 6C is incident upon a circular coupler 5, comprising a grating of concentric circles of a pitch .LAMBDA. in a radial direction which is formed on a wave guide layer 4 having an equivalent refractive index N, and has a radiation decay factor .alpha.. If .LAMBDA. and N are in a relation q.lambda./.LAMBDA.=-N wherein q is a negative integer, a phase matching condition is satisfied. If this condition is satisfied, the incident polarized beam 6C excites a waveguided light propagating in a radially outward direction and a waveguided light propagating in a radially inward direction simultaneously (this relation is called simultaneous exciting condition) and these interfere with each other resulting in a waveguided light 7 propagating in a radially outward direction. The wave guide layer 4 is formed on a transparent substrate 8 having a refractive index lower than that of the wave guide layer 4.
The polarization converting device 3 comprises a liquid crystal polarizer 3L and a phase difference film 3P as shown in FIG. 5a (see, for example, Japanese Patent laid-open publication No. H1-246808). The liquid crystal polarizer 3L has two transparent substrates 9 and 10 and a nematic liquid crystal 11 interposed between the substrates. Surfaces of one substrate 9 and the other substrate 10 formed with a polyamide film are rubbed in one direction and a rotational direction, respectively, so that the liquid crystal orients in one direction at one side thereof confronting substrate 9 and in concentric tangential directions at the other side thereof confronting substrate 10 and, accordingly, the twist angle of the molecules of the liquid crystal in a direction of the thickness thereof varies continuously in declination. When a linearly polarized beam of light having an oscillation direction which coincides with the direction of orientation of the liquid crystal 11 at the incident side is incident on a layer of the liquid crystal 11 having an optimized thickness, the plane of oscillation of the light is rotated along the twist angle of the molecules of the liquid crystal. Accordingly, the linearly polarized beam 6A is twisted in the thickness direction of the device by an angle nearly equal to the twist angle and becomes a light beam 6B having a plane of oscillation substantially coincident with the orientation direction of the molecules of the liquid crystal at the output side 10. However, since the molecules of the liquid crystal are declined at a declination line extending through the center of the device and substantially coinciding with the orientation direction at the incident side 9 and since the plane of oscillation of the light is also declined thereat, the phase of the light in one semicircular area divided by the declination line is delayed by .pi. from that of the light in the other semicircular area. In order to adjust the delay in phase, a phase difference film 3P of .lambda./2 is provided on the emission side surface of the transparent substrate 10. By aligning the boundary line 13 of the phase difference film 3P with the declination line 12, the phase of the emitted light in the one semicircular area coincides with that in the other semicircular area and, thus, a completely circumferentially polarized beam 6C is obtained.
The coupling efficiency of the incident light to the guided light, namely the ratio of an amount of the incident light to that of the guided light is given by solving so-called mode coupling equation, as known to those skilled in the art. However, since it is very complicated to solve the mode coupling equation under the simultaneous exciting condition as mentioned above, the solution is estimated by extrapolating a solution obtained by solving the mode coupling equation under a non-simultaneous exciting condition. As the result thereof, the input coupling efficiency in the case that an error d.lambda. of the wavelength, an error dN of the equivalent refractive index and an error d.LAMBDA. of the pitch are caused from the state wherein the phase matching condition is satisfied is given by the following equation provided that the incident light has an amplitude represented by a Gauss function exp{-(r/.tau.a).sup.2 } wherein r is a distance from the center axis of the coupler and assuming .kappa.=2.pi./.lambda.. EQU .eta./.sigma.e.sub.r.sup.2 =8.alpha.a{G.sub.1 (1)exp(-.alpha.a)/.tau.}.sup.2 {1-(.kappa.aN ).sup.2 H.sub.D }(1)
wherein EQU H.sub.D =G.sub.3 (5)/G.sub.1 (1)-{G.sub.2 (3)/G.sub.1 (1)}.sup.2( 2) EQU .epsilon.=dN/N-d.lambda./.lambda.+d.LAMBDA./.LAMBDA. (3) ##EQU1## EQU g.sub.P (t)=exp{-(t/.tau.).sup.2 +.alpha.at} (7) EQU g.sub.M (t)=exp{-(t/.tau.).sup.2 -.alpha.at} (8)
Radiation from the centripetal waveguided light includes a incident light and a light propagating in a reversed direction and .sigma. of the equation (1) indicates a ratio of the amount of the latter to the former. If the grating has a symmetrical cross-section, .sigma..apprxeq.1/2 in the case of two beam coupling and if a blaze grating is used, .sigma..apprxeq.1. Further, e.sub.r represents a component of oscillation in a direction of a tangent of a circle with respect to a unit electric vector of the input light. If the input light is a circumferentially polarized light beam, e.sub.r =1 and, if it is a circularly polarized light beam, e.sub.r =1/.sqroot.2. H.sub.D given by the equation (2) represents a degree of the tendency of the coupling efficiency to degrade due to errors.
The function I.sub.B used in the equations (4) to (6) represents a factor which determines a manner of the interference between the centrifugally propagating waveguided light and the centripetal propogating waveguided light both excited by the incident polarized beam 6C. If the interference is positive, namely both interfere so as to strengthen, I.sub.B =-1 (called regular phase condition). I.sub.B =0 (called single phase condition) indicates no interference and I.sub.B =1 (called reciprocal phase condition) indicates that both interfere so as to weaken.
FIGS. 6a, 6b and 6c show normalized coupling efficiencies .eta./.sigma.e.sub.r.sup.2 calculated for regular phase, single phase and negative phase conditions, respectively, which are represented as contours on a plane defined by a product .alpha.a of the radiation decay factor .alpha. and the radius "a" of the coupler and the truncation factor .tau. for the Gaussian incident light defined by a Gauss function exp{-(r/.tau.a).sup.2 }.
They take maximum values 1.438, 0.706 and 0.502 at points Pa(0.60, 0.79), Pb(1.23, 0.91) and Pc(2.26, 1.04), respectively.
FIGS. 7a, 7b and 7c show the degradation factors H.sub.D calculated for regular phase, single phase and reciprocal phase conditions, respectively, which are represented as contours on a plane defined by a product .alpha.a and the truncation factor .tau..
They take values 0.022, 0.064 and 0.025 at points Pa, Pb and Pc mentioned above.
The condition necessary to suppress the degradation of the coupling efficiency to within 20% under the maximum efficiency condition (namely, at respective points Pa, Pb and Pc) is given by the next equation. ##EQU2##
As can be understood from results obtained by the analysis mentioned above, the conventional light coupling device has disadvantages as follows.
At first, the coupling efficiency under the phase matching condition is .eta.=25% at the maximum assuming .sigma.=0.5 (see the point Pc of FIG. 6c) in the case that the incident light is concentric circularly polarized light (or radially polarized light) in which electric vectors thereof have directions opposite to each other at opposite points, whereby, phases of the guided waves excited shift by .pi. with respect to each other resulting in the negative phase condition.
Next, in order to satisfy the condition given by the equation (9), the radius a of the coupler should be smaller than 0.45.lambda./.epsilon.N (a&lt;0.45.lambda./.epsilon.N) and, accordingly, .alpha./.epsilon. should be larger than 5N/.lambda. in the case of the maximum efficiency condition (.alpha.a=2.26 at Pc of FIG. 6c). This means that .alpha./.epsilon. must be larger than 1.1.times.10.sup.4 (1/mm) when .lambda.=0.8 .mu.m and N=1.7.
This requires a technique for forming an extra-thin film having a high refractive index to obtain a large .alpha. but, in general, it is said difficult to make .alpha. larger than 50 (1/mm) in the grating coupler.
Further, since the laser diode emits light deviating in wavelength at about .+-.0.5% and the wave guide layer has an error of the equivalent refractive index of about .+-.0.5% due to inconsistencies in the thickness and the refractive index thereof, a total error .epsilon. may be estimated to be of about .+-.1%. Accordingly, the condition .alpha./.epsilon.&gt;1.1.times.10.sup.4 (1/mm) is too severe to realize. This is the second problem.